Trigonometric Graphs (Grade 11) — Worksheet & Memo

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Grade 11 · Trigonometry

Trigonometric Graphs (Grade 11)

MEMORANDUM

Name:

Class:

Date:

Mark

/ 20

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

1
Write down the amplitude of y = 2 sin x.
(1)
2✓ (1)
2
Write down the period of y = sin 2x.
(1)
360°/2 = 180°✓ (1)
3
Write down the range of y = 2 sin x.
(2)
−2 ≤ y ≤ 2✓✓ (2)
4
Describe the transformation from y = cos x to y = cos(x + 60°).
(2)
A shift of 60° to the left✓✓ (2)
5
Write down the period of y = tan 2x.
(1)
180°/2 = 90°✓ (1)
6
Write down the equations of the asymptotes of y = tan x for x ∈ [0° ; 360°].
(2)
x = 90° and x = 270°✓✓ (2)
7
How many complete cycles does y = sin 2x complete in [0° ; 360°]?
(1)
2✓ (1)
8
Write down the range of y = tan x.
(1)
y ∈ ℝ✓ (1)
9
For y = 4 sin 3x, write down the amplitude and the period, and state how many complete waves appear in [0° ; 360°].
(3)
Amplitude 4 ✓; period = 360° ÷ 3 = 120° ✓; three complete waves ✓(3)
10
Describe fully the transformation from y = cos x to y = −2 cos(x + 45°).
(3)
Amplitude becomes 2 ✓; the graph is reflected in the x-axis because a is negative ✓; and it shifts 45° to the LEFT ✓(3)
11
The graph of y = a sin kx, where a > 0 and k > 0, has amplitude 5 and period 90°. Determine a and k, and write down the equation.
(3)
a = 5 ✓; 360° ÷ k = 90° so k = 4 ✓; y = 5 sin 4x ✓(3)

TOTAL: 20 marks